Space of modular forms of level 1058, weight 4, and Character 1058.g

• Label: 1058.4.g
• Level: $1058$
• Weight: $4$
• Character orbit: 1058.g
• Rep. character: $\chi_{1058}(3,\cdot)$
• Character field: $\Q(\zeta_{253})$
• Dimension: $30360$
• Sturm bound: $552$

Defining parameters

Level:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1058.g (of order \(253\) and degree \(220\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 529 \)
Character field:			\(\Q(\zeta_{253})\)
Sturm bound:			\(552\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1058, [\chi])\).

	Total	New	Old
Modular forms	91520	30360	61160
Cusp forms	90640	30360	60280
Eisenstein series	880	0	880

Trace form

30360 * q - 8 * q^3 + 552 * q^4 - 194 * q^5 + 84 * q^6 - 84 * q^7 + 1334 * q^9 - 20 * q^10 - 34 * q^11 - 32 * q^12 - 112 * q^13 + 40 * q^14 - 744 * q^15 + 2208 * q^16 - 148 * q^17 - 40 * q^18 + 258 * q^19 + 312 * q^20 + 1060 * q^21 + 296 * q^22 + 1842 * q^23 - 32 * q^24 + 7394 * q^25 + 412 * q^26 - 272 * q^27 - 144 * q^28 - 604 * q^29 - 1016 * q^30 - 1168 * q^31 + 116 * q^33 - 520 * q^34 - 846 * q^35 + 4048 * q^36 + 1038 * q^37 - 436 * q^38 - 312 * q^39 - 80 * q^40 + 1002 * q^41 + 3800 * q^42 + 1350 * q^43 + 1152 * q^44 + 2644 * q^45 - 1564 * q^46 + 1536 * q^47 - 128 * q^48 + 12884 * q^49 - 424 * q^50 - 9988 * q^51 - 448 * q^52 - 6314 * q^53 - 3252 * q^54 - 4062 * q^55 - 1776 * q^56 - 4488 * q^57 - 1552 * q^58 + 1274 * q^59 - 72 * q^60 + 4554 * q^61 + 860 * q^62 + 9752 * q^63 + 8832 * q^64 + 4758 * q^65 + 16768 * q^66 - 10746 * q^67 + 3104 * q^68 - 846 * q^69 + 688 * q^70 + 5004 * q^71 + 1952 * q^72 + 1588 * q^73 + 3564 * q^74 + 3950 * q^75 + 152 * q^76 + 864 * q^77 - 476 * q^78 - 3178 * q^79 + 1376 * q^80 - 1232 * q^81 - 5904 * q^82 - 6808 * q^83 - 4824 * q^84 - 6654 * q^85 - 3856 * q^86 - 12344 * q^87 - 752 * q^88 + 826 * q^89 + 1176 * q^90 + 2048 * q^91 + 3804 * q^93 + 960 * q^94 + 92 * q^95 - 128 * q^96 - 11758 * q^97 - 6120 * q^98 + 466 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1058, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1058, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1058, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(529, [\chi])\)\(^{\oplus 2}\)